Corpus ID: 237581423

A Multiplicative Property for Zero-Sums II

@inproceedings{Grynkiewicz2021AMP,
  title={A Multiplicative Property for Zero-Sums II},
  author={David J. Grynkiewicz and Chao Liu},
  year={2021}
}
For n ≥ 1, let Cn denote a cyclic group of order n. Let G = Cn ⊕Cmn with n ≥ 2 and m ≥ 1, and let k ∈ [0, n− 1]. It is known that any sequence of mn+ n− 1 + k terms from G must contain a nontrivial zero-sum of length at most mn+ n− 1− k. The associated inverse question is to characterize those sequences with maximal length mn + n − 2 + k that fail to contain a nontrivial zero-sum subsequence of length at most mn + n − 1 − k. For k ≤ 1, this is the inverse question for the Davenport Constant… Expand
1 Citations
A Multiplicative Property for Zero-Sums I
Let G = (Z/nZ)×(Z/nZ) and let k ∈ [0, n−1]. We study the structure of sequences of terms from G with maximal length |S| = 2n− 2+ k that fail to contain a nontrivial zero-sum subsequence of length atExpand

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Let G = (Z/nZ)×(Z/nZ) and let k ∈ [0, n−1]. We study the structure of sequences of terms from G with maximal length |S| = 2n− 2+ k that fail to contain a nontrivial zero-sum subsequence of length atExpand
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TLDR
It is proved that the sequence (D"k(G))"k"@?"N is eventually an arithmetic progression with difference exp(G), and several questions arising from this fact are investigated. Expand
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